Solving systems of equations by substitution

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables that are solved simultaneously.

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What does it mean to solve a system of equations by substitution?

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Solving a system of equations by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

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What is the first step in solving a system of equations by substitution?

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The first step is to isolate one variable in one of the equations.

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What does it indicate if two lines represented by a system of equations are parallel?

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If two lines are parallel, it indicates that the system of equations has no solution.

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What is the solution to a system of equations?

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The solution to a system of equations is the point (or points) where the equations intersect, representing the values of the variables that satisfy all equations in the system.

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How can you determine if a system of equations has infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning they are dependent.

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What is the graphical representation of a system of equations?

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The graphical representation of a system of equations consists of the lines corresponding to each equation plotted on a coordinate plane.

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What does it mean if a system of equations has exactly one solution?

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If a system has exactly one solution, it means the lines intersect at a single point, indicating a unique set of values for the variables.

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What is the substitution method in solving equations?

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The substitution method involves replacing a variable in one equation with an equivalent expression from another equation.

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What is the significance of the coefficients in a system of equations?

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The coefficients determine the slope and position of the lines represented by the equations, affecting their intersection.